Determine the side of a square if the area of the square is 45 more than the perimeter.

We'll note as x the side of the
square.

We'll write the formula for the area of the
square:

A = x*x = x^2

We'll
write the formula for the perimeter of the square:

P = x +
x + x + x

P = 4x

Now, we'll
write mathematically the condition imposed by
enunciation:

x^2 = 4x + 45 (area is equal to the perimeter
plus 45)

We'll subtract both sides 4x +
45:

x^2 - 4x - 45 = 4x + 45 - 4x -
45

We'll eliminate like
terms:

x^2 - 4x - 45 = 0

We'll
apply the quadratic formula:

x1 = [4+sqrt(16 +
180)]/2

x1 = (4+14)/2

x1 =
9

x2 = (4-14)/2

x2 =
-5

Since the length of the side of the square cannot be
negative, we'll reject the second root x2 =
-5.

The length of the side of the square is x
= 9.